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A274325
Number of partitions of n^5 into at most two parts.
3
1, 1, 17, 122, 513, 1563, 3889, 8404, 16385, 29525, 50001, 80526, 124417, 185647, 268913, 379688, 524289, 709929, 944785, 1238050, 1600001, 2042051, 2576817, 3218172, 3981313, 4882813, 5940689, 7174454, 8605185, 10255575, 12150001, 14314576, 16777217
OFFSET
0,3
FORMULA
Coefficient of x^(n^5) in 1/((1-x)*(1-x^2)).
a(n) = A008619(n^5).
a(n) = (3 + (-1)^n + 2*n^5)/4.
a(n) = 5*a(n-1) - 9*a(n-2) + 5*a(n-3) + 5*a(n-4) - 9*a(n-5) + 5*a(n-6) - a(n-7) for n > 6.
G.f.: (1 - 4*x + 21*x^2 + 41*x^3 + 46*x^4 + 15*x^5) / ((1-x)^6*(1+x)).
E.g.f.: ((2 + x + 15*x^2 + 25*x^3 + 10*x^4 + x^5)*cosh(x) + (1 + x + 15*x^2 + 25*x^3 + 10*x^4 + x^5)*sinh(x))/2. - Stefano Spezia, Mar 17 2024
MAPLE
A274325:=n->(3+(-1)^n+2*n^5)/4: seq(A274325(n), n=0..50); # Wesley Ivan Hurt, Jun 25 2016
MATHEMATICA
Table[(3+(-1)^n+2*n^5)/4, {n, 0, 50}] (* Wesley Ivan Hurt, Jun 25 2016 *)
PROG
(PARI)
\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)).
b(n) = (3+(-1)^n+2*n)/4
vector(50, n, n--; b(n^5))
(Magma) [(3+(-1)^n+2*n^5)/4 : n in [0..50]]; // Wesley Ivan Hurt, Jun 25 2016
CROSSREFS
A subsequence of A008619.
Cf. A099392 (n^2), A274324 (n^3).
Sequence in context: A221329 A196806 A094944 * A108682 A031213 A196145
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jun 18 2016
STATUS
approved